* Draghi says ECB ready to inject liquidity to keep rates down
* Dudley says Fed was right to maintain stimulus, cites fiscal risks
* Euro broadly softer, dollar also under pressure
By Ian Chua
SYDNEY, Sept 24 (Reuters) - The euro nursed modest losses in Asia on Tuesday after the European Central Bank said it stood ready to do more to keep market rates down, while dovish comments from an influential Federal Reserve official kept the dollar on a leash.
The euro traded at $1.3493, having slipped 0.2 percent on Monday after ECB President Mario Draghi said the bank was prepared to inject more liquidity to keep money-market rates from rising to levels that could hurt the economy.
Draghi's remarks came even after closely watched surveys showed business activity in the euro zone grew faster than expected this month thanks to stronger new orders, latest evidence that the economy is healing.
Central banks on both sides of the Atlantic are at pains to ensure the pace of economic recovery continues, a point made loud and clear by the Federal Reserve.
Last week, the Fed stunned markets by leaving its massive stimulus in place, despite having allowed talk of taper to flourish in the months leading up to the Sept. 17-18 meeting.
New York Fed President William Dudley, a well known dove and close ally of Fed Chairman Ben Bernanke, justified the action saying on Monday the central bank must for now continue to push hard against threats to the economy.
Dudley cited fiscal uncertainties as Congress prepares to hash out a deal to avoid a government shutdown and raise the nation's debt ceiling.
His comments kept the U.S. dollar pinned down against many currencies, leaving the dollar index hovering near a seven-month trough plumbed last week.
Against the yen, the dollar dipped to 98.76, pulling away from Monday's high around 99.36, while the euro eased to 133.26 yen from Monday's peak of 134.56.
David Rodriguez, strategist at DailyFX, expect the dollar to stay in a range given there is no clear commitment from the Fed and no timetable on when it would start to scale back stimulus.
"The fact is that Fed officials remain as data-dependent as ever; if we see big surprises out of U.S. nonfarm payrolls data and/or inflation reports, expect big dollar moves. In the meantime, we think it's unlikely that the dollar breaks to fresh lows," he wrote in a note.
Weakness in the euro and greenback benefited higher-yielding currencies such as the Australian dollar. It rose nearly a full U.S. cent to $0.9426 overnight and also gained ground on the euro, which retreated as far as A$1.4267 from a three-week peak of A$1.4485.
The Aussie was further underpinned by growing optimism that China, Australia's single biggest export market, has pulled out of a slowdown.
A measure of China's manufacturing activity on Monday grew at its fastest pace in six months in September, offering more evidence that the world's second-largest economy was regaining momentum.
Trading is likely to be light on Tuesday with no major economic data in Asia. Japanese financial markets reopen after a long weekend. In Europe, a survey of German business sentiment from the Ifo think-tank will be closely watched.